(الف \( \int(3 x+1) e^{x} d x \)

Partie 1: On considere fonction g definie sur l'intervalle \( I=10,+\infty\left[\right. \) par: \( g(x)=1+x^{2}-2 x^{2} \ln (x) \) (1) Calculer : \( \lim _{x \rightarrow 0^{+}} g(x) \) et \( \lim _{x \rightarrow+\infty} g(x) \quad \) (1pts) (2) Calculer \( g^{\prime}(x) \) pour tout \( x \in I \) puis donner le tableau des variations de \( g \) (3) Montrer que l'equation \( g(x)=0 \) admet une unique solution \( \alpha \quad \) (1pts) (4) En deduire le signe de \( g(x \) suivant les valeaur de \( x \) dans I

1. Obtenga la derivada de cada función, usando la fórmula: \( \begin{aligned} f(x)=x^{2}\end{aligned} \) \( \begin{aligned}\text { [Res. }] f(x) & =\lim _{x \rightarrow-5} \frac{(x+h)^{2}-x^{2}}{h} \\ & =\lim _{x \rightarrow 0} \frac{2 x h+h^{2}}{h} \\ & =\lim _{x \rightarrow 0}(2 x+h) \\ & =2 x\end{aligned} \) (1) \( f(x)=2 x^{2} \) \( f(x)-5 i m \)

\( y=\frac{2 x-\pi}{x \operatorname{ctg} x} \) funksiyani \( x=0 \) va \( x=\frac{\pi}{2} \) nuqtalarda uzluksizlikga tekshiring va uzilish turini aniqlang.

To find the turning point and the degree of the polynomial \( P(x)=x^{99}-1 \), let's break it

Find the area under the curve defined by \( f(x) = 2x + 1 \) between the points \( x = 1 \) and \( x = 3 \).